Concerning the Proper Use of the Standard Deviation of the Mean Tumor Diameter

Abstract

We (1) recently compared our pituitary irradiation experiments with the hypophysectomy experiments of Ball, Samuels and Simpson (2). Since the Walker 256 tumor was used in both instances this comparison appeared important. Unfortunately Ball et al did not present their data so that measures of variability could be applied. We therefore assumed that their experimental error was of the same magnitude as ours and concluded: “It appears striking that while pituitary irradiation produces no permanent cessation of (body) growth, the effect (upon tumor growth) during the period of maximum body weight retardation is as great as that produced by complete hypophysectomy.” Samuels and Ball (3) have now recalculated their data and presented them in a form capable of statistical analysis, and of comparison with our results. They conclude from their interpretation of the data that hypophysectomy 2 produces a greater retarding effect on the rate of tumor growth than has yet been demonstrated to result from pituitary irradiation. This deduction is unfortunately based upon a common but flagrant abuse of the use of the standard deviation of the mean.3 Since their difference (controls versus treated) is 4.39 times the standard deviation of the mean, whereas our difference is 3.47 times the standard deviation of the mean, they conclude their effect is greater. It is true that if both our standard deviations were of the same magnitude this line of reasoning might hold. It happens, however, that our standard deviation of the mean is greater (1.4 times greater). Actually the ratios of control tumor mean to treated tumor mean are nearly identical in the respective experiments: 18.3/27.7 = 66 per cent (Group A and E, Ball and Samuels), 23/36 = 64 per cent (Exp. VIII, Bischoff et al).